High-resolution study of 0${}^{+}$ and 2${}^{+}$ excitations in ${}^{168}\mathrm{Er}$ with the ($p,t$) reaction

Excited states in the deformed nucleus ${}^{168}\mathrm{Er}$ have been studied with high-energy resolution, in the ($p,t$) reaction, with the Munich Q3D spectrograph. A number of 25 excited $0{}^{+}$ states (four tentative) and $632^{+}$ states have been assigned up to 4.0 MeV excitation energy. This unusually rich characterization of the $0{}^{+}$ and $2{}^{+}$ states in a deformed nucleus, close to a complete level scheme, offers a unique opportunity to check, in detail, models of nuclear structure that incorporate many excitation modes. A comparison of the experimental data is made with two such models: the quasiparticle-phonon model (QPM), and the projected shell model (PSM). The PSM wave functions appear to contain fewer correlations than those of the QPM and than required by the data.

Figure 1

Spectra measured at an angle ${\theta }_L={10}^{°}$ for the ${}^{170}\mathrm{Er}$($p,t$)${}^{168}\mathrm{Er}$ reaction at 25.0 MeV. The spectra have been measured for three different magnetic field settings of the Q3D spectrograph, for integrated charges of 7.8 mC (above), 10.8 mC (middle), and 13.6 mC (bottom), for a ±20 mm$\times \pm$20 mm opening (solid angle 11.1 msr). Peak labels represent excitation energies in keV. The states assigned as $0{}^{+}$ are marked.

Figure 2

Upper part, $L=0$ and $L=2$ angular distributions predicted by DWBA calculations with a form factor that assumes the two neutrons coming from only one orbital, as specified. Lower part, kinematic correction for the same DWBA calculations. This is defined as the relative cross section values at the same angle ($5{}^{°}$ for $L=0$ and $15{}^{°}$ for $L=2$, respectively), as a function of the excitation energy of the final state.

Figure 3

Angular distributions for ${}^{168}\mathrm{Er}$ states assigned as $0^{+}$. The states are labeled with their energy in keV (see also Table ). Parentheses indicate tentative assignment. Two different symbols occuring for some states indicate different runs (measurements with different magnetic settings). The continuous curves represent DWBA calculations with a $f_{7/2}^2$ form factor, normalized to the data.

Figure 4

Angular distributions of states in ${}^{168}\mathrm{Er}$ that have not been assigned, but, because of the forward peaking, may be $0^{+}$ states.

Figure 5

Same as Fig. 3, for states assigned as $2^{+}$.

Figure 6

Relative $(p,t)$ reaction transfer strengths (corresponding to a $f_{7/2}^2$ DWBA form factor; see discussion in the text) to $0^{+}$ and $2^{+}$ states in the ${}^{168}\mathrm{Er}$ nucleus. The values for the $0^{+}$ ground state and the $2_1^{+}$ state at 79.8 keV, respectively, were normalized to 100 (Tables and ).

Figure 7

Comparison of experimental and calculated (QPM) $0^{+}$ and $2^{+}$ levels in ${}^{168}\mathrm{Er}$ (note the logarithmic $y$-axis scale).

Figure 8

Comparison of experimental and calculated (QPM) $0^{+}$ and $2^{+}$ relative level reaction strengths for the $(p,t)$ transfer. The values for the $0{}_{g.s.}^{+}$ and $2_1^{+}$ states are normalized to 100.

Figure 9

Comparison of experimental and calculated (PSM) $0^{+}$ and $2^{+}$ levels.

Figure 10

Comparison of experimental and calculated (PSM) $0^{+}$ and $2^{+}$ relative level reaction strengths for the $(p,t)$ transfer. The values for the $0{}_{g.s.}^{+}$ and $2_1^{+}$ states are normalized to 100.